BansheeEngine/Source/BansheeUtility/Math/BsMath.cpp

//********************************** Banshee Engine (www.banshee3d.com) **************************************************//
//**************** Copyright (c) 2016 Marko Pintera ([email protected]). All rights reserved. **********************//
#include "Math/BsMath.h"
#include "Math/BsVector2.h"
#include "Math/BsVector3.h"
#include "Math/BsVector4.h"
#include "Math/BsQuaternion.h"

namespace bs
{
    const float Math::POS_INFINITY = std::numeric_limits<float>::infinity();
    const float Math::NEG_INFINITY = -std::numeric_limits<float>::infinity();
    const float Math::PI = (float)4.0f * std::atan(1.0f);
    const float Math::TWO_PI = (float)(2.0f * PI);
    const float Math::HALF_PI = (float)(0.5f * PI);
	const float Math::DEG2RAD = PI / 180.0f;
	const float Math::RAD2DEG = 180.0f / PI;
	const float Math::LOG2 = std::log(2.0f);

    Radian Math::acos(float val)
    {
        if (-1.0f < val)
        {
            if (val < 1.0f)
                return Radian(std::acos(val));
            else
                return Radian(0.0f);
        }
        else
        {
            return Radian(PI);
        }
    }

    Radian Math::asin(float val)
    {
        if (-1.0f < val)
        {
            if (val < 1.0f)
                return Radian(std::asin(val));
            else
                return Radian(HALF_PI);
        }
        else
        {
            return Radian(-HALF_PI);
        }
    }

    float Math::sign(float val)
    {
        if (val > 0.0f)
            return 1.0f;

        if (val < 0.0f)
            return -1.0f;

        return 0.0f;
    }

	float Math::invSqrt(float val)
	{
		return 1.0f/sqrt(val);
	}

	float Math::fastSin0(float val)
	{
		float angleSqr = val*val;
		float result = 7.61e-03f;
		result *= angleSqr;
		result -= 1.6605e-01f;
		result *= angleSqr;
		result += 1.0f;
		result *= val;
		return result;
	}

	float Math::fastSin1(float val)
	{
		float angleSqr = val*val;
		float result = -2.39e-08f;
		result *= angleSqr;
		result += 2.7526e-06f;
		result *= angleSqr;
		result -= 1.98409e-04f;
		result *= angleSqr;
		result += 8.3333315e-03f;
		result *= angleSqr;
		result -= 1.666666664e-01f;
		result *= angleSqr;
		result += 1.0f;
		result *= val;

		return result;
	}

	float Math::fastCos0(float val)
	{
		float angleSqr = val*val;
		float result = 3.705e-02f;
		result *= angleSqr;
		result -= 4.967e-01f;
		result *= angleSqr;
		result += 1.0f;

		return result;
	}

	float Math::fastCos1(float val)
	{
		float angleSqr = val*val;
		float result = -2.605e-07f;
		result *= angleSqr;
		result += 2.47609e-05f;
		result *= angleSqr;
		result -= 1.3888397e-03f;
		result *= angleSqr;
		result += 4.16666418e-02f;
		result *= angleSqr;
		result -= 4.999999963e-01f;
		result *= angleSqr;
		result += 1.0f;

		return result;
	}

	float Math::fastTan0(float val)
	{
		float angleSqr = val*val;
		float result = 2.033e-01f;
		result *= angleSqr;
		result += 3.1755e-01f;
		result *= angleSqr;
		result += 1.0f;
		result *= val;
		return result;
	}

	float Math::fastTan1(float val)
	{
		float angleSqr = val*val;
		float result = 9.5168091e-03f;
		result *= angleSqr;
		result += 2.900525e-03f;
		result *= angleSqr;
		result += 2.45650893e-02f;
		result *= angleSqr;
		result += 5.33740603e-02f;
		result *= angleSqr;
		result += 1.333923995e-01f;
		result *= angleSqr;
		result += 3.333314036e-01f;
		result *= angleSqr;
		result += 1.0f;
		result *= val;
		return result;
	}

	float Math::fastASin0(float val)
	{
		float root = sqrt(abs(1.0f - val));
		float result = -0.0187293f;
		result *= val;
		result += 0.0742610f;
		result *= val;
		result -= 0.2121144f;
		result *= val;
		result += 1.5707288f;
		result = HALF_PI - root*result;
		return result;
	}

	float Math::fastASin1(float val)
	{
		float root = sqrt(abs(1.0f - val));
		float result = -0.0012624911f;
		result *= val;
		result += 0.0066700901f;
		result *= val;
		result -= 0.0170881256f;
		result *= val;
		result += 0.0308918810f;
		result *= val;
		result -= 0.0501743046f;
		result *= val;
		result += 0.0889789874f;
		result *= val;
		result -= 0.2145988016f;
		result *= val;
		result += 1.5707963050f;
		result = HALF_PI - root*result;
		return result;
	}

	float Math::fastACos0(float val)
	{
		float root = sqrt(abs(1.0f - val));
		float result = -0.0187293f;
		result *= val;
		result += 0.0742610f;
		result *= val;
		result -= 0.2121144f;
		result *= val;
		result += 1.5707288f;
		result *= root;
		return result;
	}

	float Math::fastACos1(float val)
	{
		float root = sqrt(abs(1.0f - val));
		float result = -0.0012624911f;
		result *= val;
		result += 0.0066700901f;
		result *= val;
		result -= 0.0170881256f;
		result *= val;
		result += 0.0308918810f;
		result *= val;
		result -= 0.0501743046f;
		result *= val;
		result += 0.0889789874f;
		result *= val;
		result -= 0.2145988016f;
		result *= val;
		result += 1.5707963050f;
		result *= root;
		return result;
	}

	float Math::fastATan0(float val)
	{
		float valueSqr = val*val;
		float result = 0.0208351f;
		result *= valueSqr;
		result -= 0.085133f;
		result *= valueSqr;
		result += 0.180141f;
		result *= valueSqr;
		result -= 0.3302995f;
		result *= valueSqr;
		result += 0.999866f;
		result *= val;
		return result;
	}

	float Math::fastATan1(float val)
	{
		float valueSqr = val*val;
		float result = 0.0028662257f;
		result *= valueSqr;
		result -= 0.0161657367f;
		result *= valueSqr;
		result += 0.0429096138f;
		result *= valueSqr;
		result -= 0.0752896400f;
		result *= valueSqr;
		result += 0.1065626393f;
		result *= valueSqr;
		result -= 0.1420889944f;
		result *= valueSqr;
		result += 0.1999355085f;
		result *= valueSqr;
		result -= 0.3333314528f;
		result *= valueSqr;
		result += 1.0f;
		result *= val;
		return result;
	}

	inline bool Math::approxEquals(const Vector2& a, const Vector2& b, float tolerance)
	{
		return fabs(b.x - a.x) <= tolerance && fabs(b.y - a.y) <= tolerance;
	}

	inline bool Math::approxEquals(const Vector3& a, const Vector3& b, float tolerance)
	{
		return fabs(b.x - a.x) <= tolerance && fabs(b.y - a.y) <= tolerance && fabs(b.z - a.z) <= tolerance;
	}

	inline bool Math::approxEquals(const Vector4& a, const Vector4& b, float tolerance)
	{
		return fabs(b.x - a.x) <= tolerance && fabs(b.y - a.y) <= tolerance && fabs(b.z - a.z) <= tolerance && 
			fabs(b.w - a.w) <= tolerance;
	}

	inline bool Math::approxEquals(const Quaternion& a, const Quaternion& b, float tolerance)
	{
		return fabs(b.x - a.x) <= tolerance && fabs(b.y - a.y) <= tolerance && fabs(b.z - a.z) <= tolerance && 
			fabs(b.w - a.w) <= tolerance;
	}

	Vector3 Math::calculateTriTangent(const Vector3& position1, const Vector3& position2, 
		const Vector3& position3, float u1, float v1, float u2, float v2, float u3, float v3)
	{
		Vector3 side0 = position1 - position2;
		Vector3 side1 = position3 - position1;

		// Calculate face normal
		Vector3 normal = side1.cross(side0);
		normal.normalize();

		// Now we use a formula to calculate the tangent. 
		float deltaV0 = v1 - v2;
		float deltaV1 = v3 - v1;
		Vector3 tangent = deltaV1 * side0 - deltaV0 * side1;
		tangent.normalize();

		// Calculate binormal
		float deltaU0 = u1 - u2;
		float deltaU1 = u3 - u1;
		Vector3 binormal = deltaU1 * side0 - deltaU0 * side1;
		binormal.normalize();

		// Now, we take the cross product of the tangents to get a vector which 
		// should point in the same direction as our normal calculated above. 
		// If it points in the opposite direction (the dot product between the normals is less than zero), 
		// then we need to reverse the s and t tangents. 
		// This is because the triangle has been mirrored when going from tangent space to object space.
		// reverse tangents if necessary.
		Vector3 tangentCross = tangent.cross(binormal);
		if (tangentCross.dot(normal) < 0.0f)
		{
			tangent = -tangent;
			binormal = -binormal;
		}

		return tangent;
	}
}